\( \text { The set of all values of } t \in R \text {, for which the matrix } \)\( \left[\begin{array}{ccc} e^t & e^…

\(
\text { The set of all values of } t \in R \text {, for which the matrix }
\)\(
\left[\begin{array}{ccc}
e^t & e^{-t}(\sin t-2 \cos t) & e^{-t}(-2 \sin t-\cos t) \\
e^t & e^{-t}(2 \sin t+\cos t) & e^{-t}(\sin t-2 \cos t) \\
e^t & e^{-t} \cos t & e^{-t} \sin t
\end{array}\right]
\)\(
\text { Invertible, is }
\)

[JEE Main 2023, 29 Jan (Shift 2)]